889 research outputs found
Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks
We study the long term evolution of magnetic fields generated by an initially
unmagnetized collisionless relativistic shock. Our 2D particle-in-cell
numerical simulations show that downstream of such a Weibel-mediated shock,
particle distributions are approximately isotropic, relativistic Maxwellians,
and the magnetic turbulence is highly intermittent spatially, nonpropagating,
and decaying. Using linear kinetic theory, we find a simple analytic form for
these damping rates. Our theory predicts that overall magnetic energy decays
like with , which compares favorably with
simulations, but predicts overly rapid damping of short wavelength modes.
Magnetic trapping of particles within the magnetic structures may be the origin
of this discrepancy. We conclude that initially unmagnetized relativistic
shocks in electron-positron plasmas are unable to form persistent downstream
magnetic fields. These results put interesting constraints on synchrotron
models for the prompt and afterglow emission from GRBs.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy
Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007;
Downsampled version for arXiv. Full resolution version available at
http://astro.berkeley.edu/~pchang/proceedings.pd
A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves
We derive an equation whose solutions describe self-consistent states of
marginal stability for a proton-electron plasma interacting with
parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating
through this marginally stable plasma will neither grow nor damp. The
dispersion relation of these waves, {\omega} (k), smoothly rises from the usual
MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow
\pm\infty. The proton distribution function has constant phase-space density
along the characteristic resonant surfaces defined by this dispersion relation.
Our equation contains a free function describing the variation of the proton
phase-space density across these surfaces. Taking this free function to be a
simple "box function", we obtain specific solutions of the marginally stable
state for a range of proton parallel betas. The phase speeds of these waves are
larger than those given by the cold plasma dispersion relation, and the
characteristic surfaces are more sharply peaked in the v\bot direction. The
threshold anisotropy for generation of ion cyclotron waves is also larger than
that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma
High Resolution Ionization of Ultracold Neutral Plasmas
Collective effects, such as waves and instabilities, are integral to our
understanding of most plasma phenomena. We have been able to study these in
ultracold neutral plasmas by shaping the initial density distribution through
spatial modulation of the ionizing laser intensity. We describe a relay imaging
system for the photoionization beam that allows us to create higher resolution
features and its application to extend the observation of ion acoustic waves to
shorter wavelengths. We also describe the formation of sculpted density
profiles to create fast expansion of plasma into vacuum and streaming plasmas
Vlasov simulation in multiple spatial dimensions
A long-standing challenge encountered in modeling plasma dynamics is
achieving practical Vlasov equation simulation in multiple spatial dimensions
over large length and time scales. While direct multi-dimension Vlasov
simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of
Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010,
http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown
promising results, in this paper we present an alternative, the Vlasov Multi
Dimensional (VMD) model, that is specifically designed to take advantage of
solution properties in regimes when plasma waves are confined to a narrow cone,
as may be the case for stimulated Raman scatter in large optic f# laser beams.
Perpendicular grid spacing large compared to a Debye length is then possible
without instability, enabling an order 10 decrease in required computational
resources compared to standard particle in cell (PIC) methods in 2D, with
another reduction of that order in 3D. Further advantage compared to PIC
methods accrues in regimes where particle noise is an issue. VMD and PIC
results in a 2D model of localized Langmuir waves are in qualitative agreement
Relativistic Landau damping of longitudinal waves in isotropic pair plasmas
Landau damping is described in relativistic electron-positron
plasmas. Relativistic electron-positron plasma theory contains
important new effects when compared with classical plasmas. For
example, there are undamped superluminal wave modes arising from
both a continuous and discrete mode structure, the former even in
the classical limit. We present here a comprehensive analytical
treatment of the general case resulting in a compact and useful
form for the dispersion relation. The classical pair-plasma case
is addressed, for completeness, in an appendix
Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons
Runaway electrons with strongly anisotropic distributions present in
post-disruption tokamak plasmas can destabilize the extraordinary electron
(EXEL) wave. The present work investigates the dynamics of the quasi-linear
evolution of the EXEL instability for a range of different plasma parameters
using a model runaway distribution function valid for highly relativistic
runaway electron beams produced primarily by the avalanche process. Simulations
show a rapid pitch-angle scattering of the runaway electrons in the high energy
tail on the time scale. Due to the wave-particle
interaction, a modification to the synchrotron radiation spectrum emitted by
the runaway electron population is foreseen, exposing a possible experimental
detection method for such an interaction
The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes
Observations show that solar activity is distributed non-axisymmetrically,
concentrating at "preferred longitudes". This indicates the important role of
non-axisymmetric magnetic fields in the origin of solar activity. We
investigate the generation of the non-axisymmetric fields and their coupling
with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model
operating in a sphere includes solar differential rotation, which approximates
the differential rotation obtained by inversion of helioseismic data, modelled
distributions of the turbulent resistivity, non-axisymmetric mean helicity, and
meridional circulation in the convection zone. We find that (1) the
non-axisymmetric modes are localised near the base of the convection zone,
where the formation of active regions starts, and at latitudes around
; (2) the coupling of non-axisymmetric and axisymmetric modes
causes the non-axisymmetric mode to follow the solar cycle; the phase relations
between the modes are found. (3) The rate of rotation of the first
non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical
Journa
Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications
We present a review of recent developments of simulations of the
Vlasov-Maxwell system of equations using a Fourier transform method in velocity
space. In this method, the distribution functions for electrons and ions are
Fourier transformed in velocity space, and the resulting set of equations are
solved numerically. In the original Vlasov equation, phase mixing may lead to
an oscillatory behavior and sharp gradients of the distribution function in
velocity space, which is problematic in simulations where it can lead to
unphysical electric fields and instabilities and to the recurrence effect where
parts of the initial condition recur in the simulation. The particle
distribution function is in general smoother in the Fourier transformed
velocity space, which is desirable for the numerical approximations. By
designing outflow boundary conditions in the Fourier transformed velocity
space, the highest oscillating terms are allowed to propagate out through the
boundary and are removed from the calculations, thereby strongly reducing the
numerical recurrence effect. The outflow boundary conditions in higher
dimensions including electromagnetic effects are discussed. The Fourier
transform method is also suitable to solve the Fourier transformed Wigner
equation, which is the quantum mechanical analogue of the Vlasov equation for
classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and
Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy,
Marseilles, France, 31 August - 4 September 200
Weak turbulence theory of the non-linear evolution of the ion ring distribution
The nonlinear evolution of an ion ring instability in a low-beta
magnetospheric plasma is considered. The evolution of the two-dimensional ring
distribution is essentially quasilinear. Ignoring nonlinear processes the
time-scale for the quasilinear evolution is the same as for the linear
instability 1/t_ql gamma_l. However, when nonlinear processes become important,
a new time scale becomes relevant to the wave saturation mechanism. Induced
nonlinear scattering of the lower-hybrid waves by plasma electrons is the
dominant nonlinearity relevant for plasmas in the inner magnetosphere and
typically occurs on the timescale 1/t_ql w(M/m)W/nT, where W is the wave energy
density, nT is the thermal energy density of the background plasma, and M/m is
the ion to electron mass ratio, which has the consequence that the wave
amplitude saturates at a low level, and the timescale for quasilinear
relaxation is extended by orders of magnitude
The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
The relationship between two different asymptotic techniques developed in
order to describe the propagation of waves beyond the standard geometrical
optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex
geometrical optics method, is addressed. More specifically, a solution of the
wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which
yields the same wavefield intensity as the complex geometrical optics method.
Such a relationship is also discussed on the basis of the analytical solution
of the wave kinetic equation specific to Gaussian beams of electromagnetic
waves propagating in a ``lens-like'' medium for which the complex geometrical
optics solution is already available.Comment: Extended version comprising two new section
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